Convergence of independent random variable sum distributions to signed measures and applications to the large deviations problem
Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 94-102
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We study properties of symmetric stable measures with index $\alpha>2,\ \ \alpha\neq 2k,\ k\in\mathbb{N}$. Such measures are signed ones and hence they are not probability measures. We show that, in some sense, these signed measures are limit measures for sums of independent random variables.
Keywords:
Large deviation problem, strictly stable random variable, limit theorems.
@article{THSP_2010_16_1_a11,
author = {N. V. Smorodina and M. M. Faddeev},
title = {Convergence of independent random variable sum distributions to signed measures and applications to the large deviations problem},
journal = {Teori\^a slu\v{c}ajnyh processov},
pages = {94--102},
publisher = {mathdoc},
volume = {16},
number = {1},
year = {2010},
language = {en},
url = {http://geodesic.mathdoc.fr/item/THSP_2010_16_1_a11/}
}
TY - JOUR AU - N. V. Smorodina AU - M. M. Faddeev TI - Convergence of independent random variable sum distributions to signed measures and applications to the large deviations problem JO - Teoriâ slučajnyh processov PY - 2010 SP - 94 EP - 102 VL - 16 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/THSP_2010_16_1_a11/ LA - en ID - THSP_2010_16_1_a11 ER -
%0 Journal Article %A N. V. Smorodina %A M. M. Faddeev %T Convergence of independent random variable sum distributions to signed measures and applications to the large deviations problem %J Teoriâ slučajnyh processov %D 2010 %P 94-102 %V 16 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/THSP_2010_16_1_a11/ %G en %F THSP_2010_16_1_a11
N. V. Smorodina; M. M. Faddeev. Convergence of independent random variable sum distributions to signed measures and applications to the large deviations problem. Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 94-102. http://geodesic.mathdoc.fr/item/THSP_2010_16_1_a11/